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107views more  DM 2008»
10 years 2 months ago
Set maps, umbral calculus, and the chromatic polynomial
Some important properties of the chromatic polynomial also hold for any polynomial set map satisfying pS(x + y) = TU=S pT (x)pU (y). Using umbral calculus, we give a formula for t...
Gus Wiseman
76views more  DM 2002»
10 years 3 months ago
Chromaticity of some families of dense graphs
For a graph G, let P(G; ) be its chromatic polynomial and let [G] be the set of graphs having P(G; ) as their chromatic polynomial. We call [G] the chromatic equivalence class of ...
Feng Ming Dong, Kee L. Teo, Charles H. C. Little, ...
69views more  DM 2002»
10 years 3 months ago
Non-chordal graphs having integral-root chromatic polynomials II
It is known that the chromatic polynomial of any chordal graph has only integer roots. However, there also exist non-chordal graphs whose chromatic polynomials have only integer r...
Feng Ming Dong, Kee L. Teo, Khee Meng Koh, Michael...
66views more  CPC 2004»
10 years 3 months ago
Two Results on Real Zeros of Chromatic Polynomials
This note presents two results on real zeros of chromatic polynomials. The first result states that if G is a graph containing a q-tree as a spanning subgraph, then the chromatic ...
Feng Ming Dong, Khee Meng Koh
106views more  ARSCOM 2005»
10 years 4 months ago
Chromatic Equivalence of Generalized Ladder Graphs
A class of graphs called generalized ladder graphs is defined. A sufficient condition for pairs of these graphs to be chromatically equivalent is proven. In addition a formula for...
Stephen Guattery, Gary Haggard, Ronald C. Read
141views more  MST 2008»
10 years 4 months ago
From a Zoo to a Zoology: Towards a General Theory of Graph Polynomials
Abstract. We outline a general theory of graph polynomials which covers all the examples we found in the vast literature, in particular, the chromatic polynomial, various generaliz...
Johann A. Makowsky
10 years 4 months ago
Euler characteristics and chromatic polynomials
Given a graph we show how to construct a family of manifolds whose Euler characteristics are the values of the chromatic polynomial of the graph at various integers. The manifolds...
Michael Eastwood, Stephen Huggett
10 years 9 months ago
Computation of Chromatic Polynomials Using Triangulations and Clique Trees
In this paper, we present a new algorithm for computing the chromatic polynomial of a general graph G. Our method is based on the addition of edges and contraction of non-edges of ...
Pascal Berthomé, Sylvain Lebresne, Kim Nguy...